1. Field of the Invention
The present invention generally relates to the process of semiconductor manufacturing. More specifically, the present invention relates to flash-based techniques for performing high-accuracy, high-efficiency mask pattern synthesis for a semiconductor manufacturing process.
2. Related Art
Dramatic improvements in semiconductor integration circuit (IC) technology presently make it possible to integrate hundreds of millions of transistors onto a single semiconductor IC chip. These improvements in integration densities have largely been achieved through corresponding improvements in semiconductor manufacturing technologies. Semiconductor manufacturing technologies typically include a number of processes which involve complex physical and chemical interactions. Since it is almost impossible to find exact formulae to predict the behavior of these complex interactions, developers typically use process models which are fit to empirical data to predict the behavior of these processes. In particular, various process models have been integrated into Optical Proximity Correction (OPC)/Resolution Enhancement Technologies (RET) for enhancing imaging resolutions during optical lithographic processes.
More specifically, during an OPC/RET simulation process, one or more process models are used to make corrections to a semiconductor chip layout in a mask to compensate for the undesirable effects of complex lithographic processes. An OPC/RET model (“OPC model” hereafter) is typically composed of a physical optical model and an empirical process model. An OPC simulation engine uses the OPC model to iteratively evaluate and modify edge segments in the mask layout. In doing so, the OPC simulation engine computes the correct mask patterns which produce physical patterns on a wafer that closely match a desired design layout.
Note that the physical process of a pattern image transferring through an optical lithography system onto a wafer can be modeled by convolving the pattern layout with a sequence of lithography system models (i.e., lithography model kernels). In practice, an input pattern layout is typically sampled at specific locations and the resulting physical image is only evaluated at those sampled locations (particularly on or proximate to the pattern boundaries). Consequently, most model-based OPC engines and other physical verification tools require computational methods to perform numerical convolutions.
Previously, a pattern layout was typically sampled “sparsely” with only a few evaluation points on the edges of a design feature. Hence, prior art model-based OPC tools were generally designed to perform “sparse” numerical convolutions with high efficiency. One type of “sparse” convolution technique (referred to as a “flash”-based technique) involves precomputing convolution values for a set of geometric primitives and storing the precomputed values in lookup tables. For example, this flash-based technique is described in “Proximity Correction Software for Wafer Lithography,” U.S. Pat. No. 6,289,499 and in “Proximity Correction System for Wafer Lithography,” U.S. Pat. No. 6,081,685, both by inventors Michael L. Rieger and John P. Stirniman. Note that for sparse simulations, a flash-based technique can be significantly more efficient than a DFT-based (discrete Fourier transform) convolution technique, such as using fast Fourier transforms (FFTs). (We refer to a model-based OPC technique that uses a flash-based convolution method as a “flash-based OPC” technique.)
However, the number of sampling points (i.e., the density of the sampling grid) has been increasing rapidly. This is because designers have become increasingly more interested in getting simulation results at locations other than just from the edges. For example, a simulation which uses a high-density sampling grid can be used to compute slopes and detect side-lobe printing problems.
A field-based OPC simulation technique is a dense pixel-based OPC technique that provides computational efficiencies when a larger number of model evaluation locations are needed, and when the simulation layout geometry is complex. More specifically, a field-based OPC simulation technique first establishes a uniform grid of simulation points, or pixels, for an entire region of interest (typically a square area between 40 mm and 100 mm), wherein the grid spacing is determined by the spatial bandwidth required by the OPC model. Note that when the Nyquist criterion is used to establish the grid spacing, the sample array completely describes the band-limited system, and any off-grid point can be accurately calculated with appropriate interpolation methods. The field-based OPC simulation technique then computes results, in one operation, for the entire grid of simulation points. In particular, this can involve computing numerical convolutions in the frequency domain using a DFT-based technique.
Unfortunately, adopting a DFT-based technique to perform an OPC simulation is problematic because the pattern layout is non-bandlimited. More specifically, mask patterns are represented by polygons, which are mathematically represented by two-dimensional (2D) functions of surfaces. When the polygon functions are directly sampled, arrays of ones and zeros are created, which contain frequencies well above the band-limit required by the DFT engine. Hence, prior to sending the sampled data to the DFT engine, it is necessary to convert a non-bandlimited signal (i.e., the pattern layout) into a band-limited one which is required by the DFT engine.
Typically, this conversion can be performed by filtering the pattern layout using an anti-aliasing (AA) filter, which also involves a convolution operation. Because the DFT engine requires band-limited input, it cannot be used for this operation. One technique for performing the filtering operation is referred to as “subresolution-pixel” or “sub-pixel” sampling (SPS), wherein an input image is first rendered into a high-density pixel grid, which is subsequently converted to a desired lower resolution grid by sampling with a finite impulse response (FIR) filter. Note that the SPS technique is a general image processing technique, which is often used for creating visually pleasing computer graphic display images. However, the alias-noise suppression level (typically less than 1 part in 1000) required for lithography simulation would require a very fine sub-sample grid, thus making the SPS technique computationally expensive for this application.
Hence, what is needed is a method and an apparatus for converting a non-bandlimited pattern layout into a band-limited pattern image without the above-described problems.